Study of the Metrology Frame

1. Flexibility of the reference mirror

1 Flexibility of the reference mirror

In this section we wish to see how a flexibility between the nano-hexapod’s top platform and the reference mirror will change the plant dynamics and limits the performance.

First, we identify the dynamics of the system for an infinitely rigid reference mirror, and then for a reference mirror with a limited resonance frequency.

We will compare the two dynamics and conclude.

1.1 Initialization

We initialize all the stages with the default parameters.

  initializeGround();
  initializeGranite();
  initializeTy();
  initializeRy();
  initializeRz();
  initializeMicroHexapod();
  initializeAxisc();
  initializeNanoHexapod();

We first consider a rigid Sample to simplify the analysis.

  initializeSample('type', 'rigid');

1.2 Rigid fixation between the metrology frame and the nano-hexapod

Let’s first consider a rigid reference mirror and we identify the dynamics of the system.

  initializeMirror('type', 'rigid');

1.3 Flexible fixation between the metrology frame and the nano-hexapod

We now initialize a reference mirror with a main resonance frequency at \(200\ [Hz]\).

  initializeMirror('type', 'flexible', 'freq', 200*ones(6,1));

And we re identify the plant dynamics.

1.4 Comparison

The obtained transfer functions from \(\mathcal{F}_z\) to \(\mathcal{X}_z\) when considering a rigid reference mirror and a flexible one are shown in Figure 1.

Figure 1: Effect of the mirror flexibility on the transfer function from \(\mathcal{F}_z\) to \(\mathcal{X}_z\)

1.5 Conclusion

A flexibility between the nano-hexapod top platform and the reference mirror will appear in the plant as two complex conjugate poles at the frequency of the resonance of the mirror on top of the nano-hexapod. This induces 180 degrees of phase drop on the plant and will limit the attainable controller bandwidth.

This phase drop appears whatever the nano-hexapod stiffness. Thus, care should be taken when designing the fixation of the reference mirror on top of the nano-hexapod.